The current-voltage characteristics of a molecular wire linked to metallic electrodes has been the subject of much recent study. In particular, the extensive work of Mujica, Ratner et al. (1-4) and of Datta et al. (5) provides explicit formalisms in the low-temperature ballistic limit. In the first part of this work, we examine the consequences of some of the simplifying assumptions of these approaches, with particular reference to the system of p-thioquinone linked to Au electrodes at the 111 faces. We proceed by considering the electrode to be represented by a supramolecular cluster, an approach also used by Emberly and Kirczenow (6) and by Datta et al. (5). Only a small number of surface Au atoms, those nearest the binding sites, need to be explicitly included in the supramolecular cluster. The topics considered include the following:

The consequences of using Newns-Anderson semi-elliptical model densities of states or constant densities, rather than actual bulk state densities.

The consequences of ignoring p and d band states

The consequences of ignoring the real component in the Green's function self-energy terms

The consequences of using one-electron tight-binding models of electronic structure: comparisons with density functional and related approaches.

Examination of the form of scaling of current with magnitude of molecule-electrode coupling.

In the second part of this work, analytical models are developed for the conductance of linear molecules which both simplify earlier expressions and bring out fundamental relationships in a particularly transparent fashion.